Which symmetry follows Ward-Takahashi identity?

[ndung200790]

Please teach me this:
It seem to me the Ward-Takahashi is validated by the renormalization, if the theory can not be renormalized the proof of Ward identity is failed.In QED the Ward identity is validated by electrical charge renormalization.
The Ward-Takahashi implies a current conservation,then it is the result of a symmetry.But I do not know which symmetry it is. E.g in QED which symmetry the Ward-Takahashi implies?
Thank you very much in advanced.

 

[DrDu]

E.g in QED which symmetry the Ward-Takahashi implies?
Thank you very much in advanced.

The U(1) gauge symmetry of electric charge.

 

[ndung200790]

Why we know that current of conservation is a electrical current?

 

[ndung200790]

Thank Dr Du very much! Now I understand that U(1) symmetry leads to Ward identity in QED.

 

[oraclelive]

sorry I've got no idea.

 

[DrDu]

Sorry, maybe I don't understand what you mean. I know the WT identities as a clever trick to use current conservation to derive some set of diagrams which fulfill the corresponding gauge symmetry. But the relation between the current conservation and the symmetry follows from Noethers theorem.

 

[ndung200790]

The Noether theorem says that a symmetry corresponds with a classical current conservation.But what it says about a corresponding quantum current?

 

[ndung200790]

In QFT book of Peskin&Schroder at 7.4 section saying Ward Identity is the diagrammatic expression of the conservation of the electric current...Ward Identity imposes the symmetry of quantum mechanical amplitudes. But I do not understand why the current is the electric current(we are considering QED) and I think the symmetry corresponding with Ward Identity(with the corresponding current) is some symmetry of Lagrangian of the theory but not of the diagrams

 

[ndung200790]

Sorry ''Ward Identity imposes the symmetry of quantum mechanical amplitudes'' is not correct.It is ''Ward Identity imposes the symmetry on quantum mechanical amplitude'', so it is OK.Please forgive my mistake.My English is still week,I am Vietnamese.

 

[ndung200790]

At the moment,I think the symmetry for a current conservation neednot a symmetry of the Lagrangian of the theory,but it may be symmetry of the diagrams.Because Noether theorem neednot only be applyed for Lagrangian of the theory.

 

[ndung200790]

In QFT book of Schroder&Peskin at chapter 9.6,now I understand that by Schwinger-Dison eqn,the conservation current equation(considering in quantum regime) and the equation of motion(quantum regime)are ultimately related:all eqns of current conservation fulfil the equation of motion.The Ward-Takahashi is only the quantum conclusions of Noether theorem applying on Lagrangian.So the Ward-Takahashi in QED is a representation of electric current conservation(quantum regime) which is a result of U(1) symmetry.
Please teach me whether my thinking is correct?

 

[voltan]

I have got the following question, in the first place: Does Ward-Takahashi identity follow from local or global gauge invariance?

Thanks!

 

[andrien]

electrodynamics results from local gauge invariance.(yang-mills)